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Difference of The Squares

The difference of the squares of two consecutive numbers is equal to the sum of two numbers: As:

(i) 3 x 3 – 2 x 2 = 3 + 2 = 5

(ii) 9 x 9 – 8 x 8 = 9 + 8 = 17

(iii) 25 x 25 – 24 x 24 = 25 + 24 = 49

(iv) 217 x 217 – 216 x 216 = 217 + 216 = 433


You may write the difference of the squares of two given consecutive numbers:

(i) 76 x 76 – 75 x 75 = _______ .

(ii) 115 x 115 – 114 x 114 = _______ .

(iii) 137 x 137 – 136 x 136 = _______ .

(iv) 376 x 376 – 375 x 375 = _______ .

(v) 695 x 695 - 694 x 694 = _______ .


Check the answers: 

(i) 76 x 76 – 75 x 75

= 76 + 75

= 151.

Answer: 151


(ii) 115 x 115 – 114 x 114

= 115 + 114

= 229.

Answer: 229



(iii) 137 x 137 – 136 x 136

= 137 + 136

= 273.

Answer: 273



(iv) 376 x 376 – 375 x 375

= 376 + 375

= 751.

Answer: 751



(v) 695 x 695 - 694 x 694

= 695 + 694

= 1389.

Answer: 1389

Related Concept

● Patterns and Mental Mathematics

● Counting Numbers in Proper Pattern

● Odd Numbers Patterns

● Three Consecutive Numbers

● Number Formed by Any Power

● Product of The Number

● Magic Square

● Square of a Number

● Difference of The Squares

● Multiplied by Itself

● Puzzle

● Patterns

● Systems of Numeration








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